code: def lineseg_integrate(polygon, index, line_seg, expr, degree):
      """Helper function to compute the line integral of ``expr`` over ``line_seg``.
  
      Parameters
      ===========
  
      polygon :
          Face of a 3-Polytope.
      index :
          Index of line_seg in polygon.
      line_seg :
          Line Segment.
  
      Examples
      ========
  
      >>> from sympy.integrals.intpoly import lineseg_integrate
      >>> polygon = [(0, 5, 0), (5, 5, 0), (5, 5, 5), (0, 5, 5)]
      >>> line_seg = [(0, 5, 0), (5, 5, 0)]
      >>> lineseg_integrate(polygon, 0, line_seg, 1, 0)
      5
      """
      expr = _sympify(expr)
      if expr.is_zero:
          return S.Zero
      result = S.Zero
      x0 = line_seg[0]
      distance = norm(
          tuple([line_seg[1][i] - line_seg[0][i] for i in range(3)])
      )
      if isinstance(expr, Expr):
          expr_dict = {
              x: line_seg[1][0],
              y: line_seg[1][1],
              z: line_seg[1][2],
          }
          result += distance * expr.subs(expr_dict)
      else:
          result += distance * expr
  
      expr = (
          diff(expr, x) * x0[0]
          + diff(expr, y) * x0[1]
          + diff(expr, z) * x0[2]
      )
  
      result += lineseg_integrate(
          polygon, index, line_seg, expr, degree - 1
      )
      result /= degree + 1
      return result
  
imports: from functools import cmp_to_key
  from sympy.abc import x, y, z
  from sympy.core import S, diff, Expr, Symbol
  from sympy.core.sympify import _sympify
  from sympy.geometry import Segment2D, Polygon, Point, Point2D
  from sympy.polys.polytools import LC, gcd_list, degree_list, Poly
  from sympy.simplify.simplify import nsimplify
label_desc: Use image node_id 8 for calling a global function with example usage: lineseg_integrate(polygon, index, line_seg, expr, degree) and returns: result, S